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The behavior of the Mordell-Weil group of elliptic curves
Authors:
Armand Brumer and Oisín McGuinness
Journal:
Bull. Amer. Math. Soc. 23 (1990), 375-382
MSC (1985):
Primary 11G40; Secondary 11D25, 11G05, 11-04, 14K15
MathSciNet review:
1044170
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References |
Similar Articles |
Additional Information
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- 1.
- B. Birch and W. Kuyk, editors, Modular functions of one variableIV, Lecture Notes in Math., vol. 476, Springer-Verlag, New York, 1975. MR 376533
- 2.
- A. Brumer and K. Kramer, The rank of elliptic curves, Duke Math. J. 44 MR 457453
- (1977), 715-743.
- 3.
- J. Buhler, B. H. Gross and D. B. Zagier, On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank3, Math. Comp. 44 (1985), 473-481. MR 777279
- 4.
- H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields (II), Proc. Royal Soc. London Ser. (A) 322 (1971), 405-420. MR 491593
- 5.
- D. M. Goldfeld, Conjectures on elliptic curves over quadratic fields, Number Theory Carbondale 1979, Lecture Notes in Math., vol. 751, Springer-Verlag, New York, 1979, pp. 108-118. MR 564926
- 6.
- F. Gouvea and B. Mazur, The square-free sieve and the rank of Mordell-Weil, preprint, April 1989.
- 7.
- D. Grayson, The arithogeometric mean, Arch. Math. 52 (1989), 507-512. MR 998624
- 8.
- G. Kramarz and D. B. Zagier, Numerical investigations related to the L -series of certain elliptic curves, J. Indian Math. Soc. 52 (1987), 51-60, (Ramanujan Centenary volume). MR 989230
- 9.
- B. Mazur, Modular curves and the Eisenstein ideal, Publ. Math. IHES 47 (1977), 33-186. MR 488287
- 10.
- J.-F. Mestre, Formules explicites et minorations de conducteurs de variétés algébriques, Comp. Math. 58 (1986), 209-232. MR 844410
- 11.
- J.-F. Mestre, La méthode des graphes. Exemples et applications, Class Numbers and Units of Number Fields, Katata conference, Nagoya University, Nagoya, Japan, 1986, pp. 217-242, (unpublished tables). MR 891898
- 12.
- J.-F. Mestre and J. Oesterlé, Courbes de Weil semi-stables de discriminant une puissance m-ième, J. Reine Angew. Math. 400 (1989), 173-184. MR 1013729
- 13.
- J. Quer, Corps quadratiques de 3- rang 6 et courbes elliptiques de rang 12, C. R. Acad. Sci. Paris Ser. 1 305 (1987), 215-218. MR 907945
- 14.
- K. Rubin, The work of Kolyvagin on the arithmetic of elliptic curves, Arithmetic of Complex Manifolds (W. P. Barth and H. Lange, eds.), Lecture Notes in Math., vol. 1399, Springer-Verlag, New York, 1989, pp. 128-136. MR 1034261
- 15.
- J. H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Math, vol. 106, Springer-Verlag, New York, 1986. MR 817210
- 16.
- J. H. Silverman, Computing heights on elliptic curves, Math. Comp. 51 (1988), 339-358. MR 942161
- 17.
- J. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179-206. MR 419359
- 18.
- L. C. Washington, Number fields and elliptic curves, NATO Adv. Study Inst, on Number Theory, Banff 1988, Kluwer, Netherlands, 1989, pp. 245-278. MR 1123077
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1990-15937-3
PII:
S 0273-0979(1990)15937-3
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